GATE CE 2022 Set 1 — Question 44
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Transportation Engineering → Traffic Studies & Flow → Speed-Density-Flow
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Question
Consider the four points P, Q, R, and S shown in the Greenshields fundamental speed-flow diagram. Denote their corresponding traffic densities by , and , respectively. The correct order of these densities is
Correct answer
(A) k_P k_Q k_R k_S
Solution
In the Greenshields model, the relationship between speed () and density () is linear: , where is free-flow speed and is jam density. Flow () is given by . This results in a parabolic relationship between speed and flow.
- Point S: Corresponds to the highest speed (free-flow speed ). At this point, density .
- Point R: Located on the upper limb of the curve (uncongested regime). Speed is high, so density is low but greater than .
- Point Q: Corresponds to the maximum flow (capacity). At capacity, speed and density .
- Point P: Corresponds to zero speed. At this point, the density is the jam density .
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